The Torah says (Numbers 15:37-40), "You shall make tassels on the corners of your garments..." These tassels, called tzitzit, are spun and knotted to remind us of the commandments. The numerical value of the letters in the Hebrew word tzitzit is 600. Adding the eight tassels and the five knots of each tzitzit, the total is 613. Therefore, it is customary to wear the tzitzit outside of one's clothing, in plain sight. Having a tangible reminder of the 613 commandments strengthens our control over the temptations of the heart.
Only garments with four (or more) points require tzitzit, and since few garments today (except ponchos) have four points, we wear a special garment called a tallit katan to fulfill this precept. During morning prayers, a larger version of this same garment, the tallit gadol, is worn.
Technically speaking, Tzitzit are applied during the day, but, according to Kabbalah, they should be worn even when one sleeps at night.